In particular, the central piece of object of my scientific study is  "group of diffeomorphism in connection with problems of mathematical physics". Following works are of principal importance to my scientific research investigation

• Infinite dimensional geometry of group of diffeomorphism and fluid flow (inspired by classical work of Arnold, Marsden, Ebin and in recent times C.D. Lellis, Boris Khesin, Alexander Shinrelman)

• "Reasonable volume preserving"  version of some particular theorems of dynamics of diffeomorphism group. This work is inspired by question posed by Arnold in 1981 and a recent work of Andrei Agrachev. 

• Group of Diffeomorphism and Geometric Control Theory (A problem that was asked to me  by Andrei Agrachev). This has occupied me for last few years. 

• Diffeomorphsim Groups, Hydrodynamics and Relativity written by Jerrold E. Marsden, David Ebin, Arthur E. Fischer and related work of Marsden, Arnold, Alexander Schinrelman, Boris Khesin, Stephen Priston